TITLE:
Euler Equation with Auxiliary Condition
AUTHORS:
Haiduke Sarafian
KEYWORDS:
Lagrange Equations of the First Kind, Differential-Algebraic-Equation (DAE), Computer Algebra System, Mathematica
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.16 No.4,
October
19,
2026
ABSTRACT: This research-oriented report applies Lagrange’s Equations of the First Kind to analyze three examples. The examples are categorized by the symmetry of the tracks in a two-dimensional vertical plane that a massive point-like particle traverses. The time-dependent coordinates of the mobile point traversing the tracks are determined. The equation of motion embodies a second-order differential-algebraic equation (DAE). Using the Computer Algebra System (CAS) Mathematica, the equations are solved numerically. Auxiliary by-products, such as the effective forces and associated kinematic quantities, are quantified, determined, and extensively graphed. Most of the essential Mathematica code for reproduction and potentially augmenting the scale of interest and generalization on a need basis is embodied. The latter assists Mathematica-familiar readers in exercising the code.